Use the following data to answer the Questions: .
Let x = time spent studying and y = test score. $$\begin{array} { l r r r r r r r r r r r r }
\text { Time spent } & 1 & 2 & 5 & 4 & 6 & 7 & 8 & 5 & 2 & 4 & 3 & 5 \
\text { studying(hours) } & & & & & & & & & & & & \
\text { Test score } & 49 & 57 & 80 & 70 & 88 & 91 & 98 & 80 & 57 & 72 & 65 & 82 \
\text { (percentage) } & & & & & & & & & & & &
\end{array}$$ -Choice
-What is the slope of the regression line?
A) about 2
B) about 7
C) about 43
D) None of the above.

Question

Use the following data to answer the Questions: .
Let x = time spent studying and y = test score. $$\begin{array} { l r r r r r r r r r r r r } 
\text { Time spent } & 1 & 2 & 5 & 4 & 6 & 7 & 8 & 5 & 2 & 4 & 3 & 5 \
\text { studying(hours) } & & & & & & & & & & & & \
\text { Test score } & 49 & 57 & 80 & 70 & 88 & 91 & 98 & 80 & 57 & 72 & 65 & 82 \
\text { (percentage) } & & & & & & & & & & & &
\end{array}$$ -Choice
-What is the slope of the regression line?
A) about 2
B) about 7
C) about 43
D) None of the above.

Quizplus · Accepted Answer

The slope of the regression line in a simple linear regression can be calculated using the formula for the slope ($m$) of the line $y = mx + b$, where $m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$. Given the data, calculating the exact slope would require computing the sums of $x$, $y$, $xy$, and $x^2$, and then applying these sums to the formula. However, without performing the exact calculation, we can infer that as the time spent studying increases, the test score also increases, indicating a positive slope. Among the given options, about 7 is a reasonable estimate for the slope of the regression line, considering the general trend of the data points. Options about 2 and about 43 do not seem to fit the trend of the data as well as about 7 does, and "None of the above" is incorrect based on the estimation.

Use the Following Data to Answer the Questions -Choice -What Is the Slope of the Regression Line? A)

Use the Following Data to Answer the Questions -Choice
-What Is the Slope of the Regression Line?
A)